But I keep wondering how Fenton planned the execution of the FBI agent from the get-go.

You see he happens to be a sheriff somehow and he must've asked his wife (which conveniently happens to be working for him at the sheriff office/station) to answer any calls with a re-assuring tone, to dismiss and lower the level of any alert that may be caused by the FBI agent when he calls to inquire about him.

But what if the FBI agent calls someone else?

It is almost like Fenton knew that in advance, and were counting on the FBI not to involve anyone else, so that he could later seclude him and kill him.

I know that Fenton is "gifted" somehow and CCTV cameras don't get a clear shot of his face, and that's supposed to be an assistance "from God", but does the assistance also include knowing the actions and stupidity of "victims/sinners" beforehand?

If so, then why go through the trouble of killing them in this manner? Why not a more subtle way? Is it only for the sake of having a thriller movie?

Is there any reason other than this is a movie and it was written that way?

Since Adam introduced himself as Fenton at the FBI office, he knows
that the investigation of Doyle's disappearance will center on Fenton.
The authorities will discover that Fenton was the God's Hand serial
killer and conclude that Doyle became one of his victims.

Having arrived at the rose garden with Doyle, Meiks confesses that he
is Adam and that he has destroyed Fenton, who grew up to become the
God's Hand serial killer, as a demon.

Adam was aware that not only could security cameras not record his image, but nobody could remember his face, even seeing him in person.

Those who saw Meiks at the FBI office, including Agent Griffin Hull,
inexplicably remember nothing about "Fenton" Meiks' appearance.
Surveillance videotapes all have a distortion when played that
obscures Meiks' face. The investigation then proceeds as Adam had
predicted.

After Adam reveals who he actually is to agent Doyle, he informs agent Doyle that he is a demon and that he is on the list to be destroyed.

When he touches Doyle, a new vision reveals that Doyle had murdered
his own mother. Meiks tells a dazed Doyle that Doyle's name was given
to him on the list of demons to be destroyed.

Adam kills his victims in this manner because that is the original "vision" that his father had when visited by the angel. All victims must be buried in the Rose Garden.

The father's modus operandi is to wait for the angel to give him a
list of names of those who must be destroyed. He then abducts an
individual from the list, takes them to the family home and, with his
sons present, touches them, which, he says, grants him a vision of the
crimes the demon has committed. He then finishes the victim with an ax
and buries the body in the rose garden.

Although Adam does not know the actual sins that the "demons" committed, he does receive their names in his "visions".

You had stated that Adam is "gifted". The main thing to remember is that Adam is "protected" by God. He is above the law and cannot be identified because of God's help and protection. It would not matter if the FBI agent called somebody else.